Strong Convergence Theorems of Viscosity Iterative Algorithms for Split Common Fixed Point Problems

Abstract

In this paper, we propose a viscosity approximation method to solve the split common fixed point problem and consider the bounded perturbation resilience of the proposed method in general Hilbert spaces. Under some mild conditions, we prove that our algorithms strongly converge to a solution of the split common fixed point problem, which is also the unique solution of the variational inequality problem. Finally, we show the convergence and effectiveness of the algorithms by two numerical examples.

Keywords

• strong convergence
• viscosity iterative algorithm
• split common fixed point problem
• nonexpansive mapping
• averaged mapping
• bounded perturbation resilience
• variational inequality problem